During peeling of a soft elastic strip from a substrate, strong adhesional forces act locally inside the peeling zone. It is shown here that when a standard contact finite element (FE) formulation is used to compute the peeling process, a large mesh refinement is required since the numerical solution procedure becomes unstable otherwise. To improve this situation, several different efficient enrichment strategies are presented that provide stable solution algorithms for comparably coarse meshes. The enrichment is based on the introduction of additional unknowns inside the contact elements discretizing the slave surface. These are chosen in order to improve the approximation of the peeling forces, while keeping the overall number of degrees of freedom low. If needed, these additional unknowns can be condensed out locally. The enrichment formulation is developed for both 2D and 3D nonlinear FE formulations. The new enrichment technique is applied to the peeling computation of a gecko spatula. The proposed enriched contact element formulations are also investigated in sliding computations. Copyright © 2011 John Wiley & Sons, Ltd.